The categorical Gini correlation, $\rho_g$, was proposed by Dang et al. to measure the dependence between a categorical variable, $Y$ , and a numerical variable, $X$. It has been shown that $\rho_g$ has more appealing properties than current existing dependence measurements. In this paper, we develop the jackknife empirical likelihood (JEL) method for $\rho_g$. Confidence intervals for the Gini correlation are constructed without estimating the asymptotic variance. Adjusted and weighted JEL are explored to improve the performance of the standard JEL. Simulation studies show that our methods are competitive to existing methods in terms of coverage accuracy and shortness of confidence intervals. The proposed methods are illustrated in an application on two real datasets.

翻译：分类吉尼相关系数 $\rho_g$ 由 Dang 等人提出，用于衡量分类变量 $Y$ 与数值变量 $X$ 之间的依赖关系。研究表明，$\rho_g$ 相较于现有依赖度量方法具有更优的性质。本文针对 $\rho_g$ 发展了刀切经验似然方法。在不估计渐近方差的情况下，构建了吉尼相关系数的置信区间。为改进标准 JEL 的性能，我们探索了调整型与加权型 JEL 方法。模拟研究表明，本方法在覆盖精度和置信区间长度方面优于现有方法，并通过两个实际数据集的应用实例展示了所提方法的有效性。